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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Kondo model ： ウィキペディア英語版 Kondo model The Kondo model (sometimes referred to as the s-d model) is a model for a quantum impurity coupled to a large reservoir of noninteracting electrons. The quantum impurity is represented by a spin-1/2, which is coupled to a continuous band of noninteracting electrons by an antiferromagnetic exchange coupling, J. The Kondo model is used as a model for metals containing magnetic impurities, as well as quantum dot systems. $H\; =\; \backslash sum\_\; \backslash epsilon\_\_c\_\; -\; J\; \backslash mathbf(0)\backslash cdot\; \backslash mathbf$ where $\backslash mathbf$ is a spin-1/2 operator representing the impurity, and $\backslash mathbf(0)\; =\; \backslash sum\_\; c^\_\; \backslash mathbf\_c\_$ is the local spin-density of the noninteracting band at the impurity site ($\backslash mathbf$ are the Pauli matrices). J < 0, i.e. the exchange coupling is antiferromagnetic. Jun Kondo applied third-order perturbation theory to the Kondo model and showed that the resistivity of the model diverges logarithmically as the temperature goes to zero. This explained why metal samples containing magnetic impurities have a resistance minimum (see Kondo effect). The problem of finding a solution to the Kondo model which did not contain this unphysical divergence became known as the Kondo problem. A number of methods were used to attempt to solve the Kondo problem. Phillip Anderson devised a perturbative renormalization group method, known as Poor Man's Scaling, which involves perturbatively eliminating excitations to the edges of the noninteracting band. This method indicated that, as temperature is decreased, the effective coupling between the spin and the band, $J\_\{\backslash mathrm\{eff\}\}$, increases without limit. As this method is perturbative in J, it becomes invalid when J becomes large, so this method did not truly solve the Kondo problem, although it did hint at the forward. The Kondo problem was finally solved when Kenneth Wilson applied the numerical renormalization group to the Kondo model and showed that the resistivity goes to a constant as temperature goes to zero. There are many variants of the Kondo model. For instance, the spin-1/2 can be replaced by a spin-1 or even a greater spin. The two-channel Kondo model is a variant of the Kondo model which has the spin-1/2 coupled to two independent noninteracting bands. One can also consider the ferromagnetic Kondo model (i.e. the standard Kondo model with J > 0). The Kondo model is intimately related to the Anderson impurity model, as can be shown by Schrieffer–Wolff transformation. ==See also== *Anderson impurity model *Kondo effect 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kondo model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.